El empirismo de John Locke

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La duda que nos lleva a la certeza (de acuerdo a Descartes)

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Mi salsa de tomate (importante para cocineros)☝️

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Can one imagine "a point" as counter to Kant's "space mind experiment?" Yes and No :)

1. In geometry: a point has zero extension, but it is not nothing

For example: In Euclidean geometry, a point is an object with position but no length, area, or volume.

So, in one dimension:

$$\text{length of a point}=0$$

That doesn't mean that the point is identical to the number $0$.

For example, imagine on a line, the points

$$-5,\quad 0,\quad 7$$

all have zero length. Yet they are different points because they occupy different positions.

So:

zero is a measure; a point is a location. 

2. In topology, the distinction becomes even clearer:

Topology doesn't fundamentally care about length, area, or volume. 

It cares about neighborhoods, continuity, connectedness, and how points relate to one another.

A topological point is an element of a space:

$$p\in X.$$

The point $p$ can have no size whatsoever and still be structurally significant.

For example, consider the interval

$$[0,1].$$

The point $0$ is a single point. Its measure is zero. But topologically it isn't equivalent to “nothing”: removing its left bound it gives

$$(0,1],$$

which is a different topological space.

Even more strikingly, removing a single point from the circle $S^1$ produces something homeomorphic to a line (sorry I cannot reproduce a drawing here), the result would be:

$$$$S1−{p}≅R.S^1-\{p\}\cong \mathbb R.

So a point can have zero size while having important structural consequences.

3. Is a point therefore “no space”?

Here we need to be careful.

A point is zero-dimensional, but that doesn't mean it is “outside space.”

A point is an element of a space.

Think of:

$$\mathbb R$$

as the space and

$$3$$

as one of its points.

The point 3 doesn't contain any interval around itself. But the space does. Every “neighborhood” of 3 contains other points:

$$(2.9,3.1).$$

This gives us an interesting distinction:

The point itself has no extension; but its neighborhood expresses its spatial situation.

Why is that?

Because dimension is not the same thing as size. 

A point has zero size in every direction, so its dimension is 0.

There are two ways to understand this: geometrically and topologically, and the topological one is more interesting.

Geometrically

A line has one independent direction:

$$\longrightarrow$$

You can move along it in one dimension. A plane has two:

$$\rightarrow \quad \uparrow$$

A point has neither. You can't move in any direction while staying within the point.

So: 

point → 0 dimensions; 

line → 1 dimension; 

plane → 2 dimensions; 

ordinary space → 3 dimensions;

This distinction becomes very important philosophically.

4. There's a beautiful distinction coming up:

Let's come back to our Kantian experiment.

 ¿Can we imagine a room without objects, but cannot imagine the room without space?

Yes! 

You can imagine a point without extension:

$$\bullet$$

but you cannot really get a spatial point without some spatial structure in which “point” has its meaning.**

However, 

A point has no space of its own. That is to say: it cannot function as a point except within a space.

That's different from saying that a point is “no space.”

___________________

** A point has zero extension, but it nevertheless has position.

Where does that position come from?

Not from the point itself.

If you opened up the point and looked inside, you'd find no spatial content explaining its position. Its position is determined ONLY relationally:

It is here rather than there.

And "here rather than there" presupposes a field of possible locations.

It doesn't mean that you need to physically draw a line around the point. 

The concept of a spatial point is incomplete without the possibility of spatial relations.

A new hypothesis in evolutionary biology challenges a prevailing consensus

A new study (2026) led by Duke University researchers, recently published in Science, challenges a long-held explanation regarding primate brain evolution. 

Richard Key is leading the new hypothesis (Kay is a professor of evolutionary anthropology).

The prevailing consensus held that the massive expansion of the neocortex—particularly the frontal regions—was linked to the development of higher cognitive abilities. 

In other words: more frontal brain → greater thinking capacity

(I'm guilty of repeating this point to my students!) 😡

The Duke University research team virtually reconstructed the brains of various fossil primates based on the spaces left inside their skulls. By comparing living and fossil species, they found that neocortical expansion correlated more closely with reliance on vision than with disproportionate frontal lobe expansion.

In other words, a large brain did not necessarily evolve first to produce more complex cognition; it was linked to processing an increasingly demanding visual world.

Do you see the "causal fallacy"—confusing correlation with causation— at play here? 

Shame? Not for the skeptic! 😉

HOW TO EXPLAIN SCIENTIFIC REVOLUTIONS

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Review for our Quiz (2025)

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Review for Quiz #1

The presocratics.

Philosophy and its branches.

Fallacies.

Mind experiments.

What is truth.

Necessary and sufficient conditions.

Criteria of Adequacy of Scientific Theories.

Logical and causal possibility.

Cause and effect. 

La futurofobia (y sus consecuencias económicas)

 1. ¿El miedo al riesgo no favorece acaso la posición competitiva de Anthropic?

Anthropic fue concebido precisamente en torno a la seguridad de la IA. 

For the sake of argument, el problema central de la IA deviene en:

¿Qué otra empresa está desarrollando modelos suficientemente poderosos sin perder el control sobre ellos?

Anthropic parece haber convertido una preocupación social en ventaja competitiva.

El mensaje está implícito:

La IA será extraordinariamente poderosa, al punto de destrucción del género humano. Por eso debemos confiar en aquellos que toman la seguridad más en serio.

¿Eso no es marketing? Aunque no necesariamente sea solo eso.

Veamos la asimetría: ¿puede o no el miedo a la IA aumentar el valor (de la especialidad) de Anthropic? 

Cuando la IA no era peligrosa, ¿no era la seguridad una prioridad secundaria? 

Y si de la noche a la mañana el peligro es catastrófico, la seguridad se convierte en... bueno...

2. El discurso apocalíptico favorece la regulación

Supongamos que desde ahora surgieran regulaciones: 

evaluaciones de seguridad, 

auditorías, 

requisitos de infraestructura, 

controles sobre modelos avanzados, 

obligaciones de reporte, etc.

¿Quién está en condiciones óptimas para ejecutarlas?

Las empresas capitalizadas que ya cuentan con equipos jurídicos, de investigación de seguridad, de infraestructura y de relaciones institucionales. 

Fenómeno clásico de la economía política: la regulación como barrera de entrada para posibles competidores.

Si Anthropic dice: "Los modelos futuros podrían desarrollar prácticas que ni siquiera comprendemos". 

Le sigue la respuesta política: "Entonces necesitamos controles más rigurosos".

Controles que dificultan mucho la entrada de nuevos competidores.  

Otra paradoja:

Anthropic puede defender una mayor regulación en nombre de la seguridad y, al mismo tiempo, beneficiarse de que dicha regulación limite a sus competidores.

Es casi un incentivo estructural.

3. El miedo desplaza la discusión de AI propiamente dicha, hacia la autoridad sobre AI

Anthropic ocupa una posición peculiar: se presenta simultáneamente como fabricante e intérprete privilegiado del problema.

El valor económico parece ser indirecto: influencia regulatoria, acceso a los gobiernos, legitimidad institucional, cobertura mediática, capacidad para atraer talento y diferenciación frente a otros laboratorios.

¿Quién gana cuando le tenemos miedo al "más allá?"  

Fallacies (watch out, most of info you get from sources is fallacious)

A fallacy is an argument which provides poor reasoning in support of its conclusion. Here are some examples:

Begging the Question: The argument's conclusion is used as one of its premises. Basically the proof is assumed.
 

A: He's mad right now.
B: How do you know?
A: Because he's really angry.

Of course smoking causes cancer. The smoke from cigarettes is a carcinogen!

Prosecutor to defendant: So how did you feel when you killed your wife?

Ad hominem (or Against the Person): When someone tries to win an argument by denigrating its presenter (favorite fallacy used by politicians and the media to put down an enemy)

"You claim that this man is innocent, but you cannot be trusted since you are a criminal as well."

"Hey, Professor Moore, we shouldn't have to read this book by Freud. Everyone knows he used cocaine."

Argumentum ad Populum (Literally "Argument to the People"): Using an appeal to popular assent, often by arousing the feelings and enthusiasm of the multitude rather than building an argument.

Ex: "The Bold and the Listless must be a great book. It’s been on the best seller list for 8 weeks."

Appeal to ignorance (ad ignorantiam): It has two forms: The fallacy occurs when you argue that your conclusion must be true, because there is no evidence against it. Ad ignorantiam wrongly shifts the burden of proof away from the one making the claim.

"She hasn't said she doesn't like you, right? So she's probably interested. Call her up."

"Nobody has conclusively proven that the Yeti doesn't exist, therefore it must exist."

 "I thought I had every reason to think I was doing fine leading the group; no one complained."
 
Hasty Generalization: You are guilty of hasty generalization when jumping into conclusion about all things of a certain type based on evidence that concerns only a few things of that type (favorite argument used by politicians and ideologues).  

"The department of law enforcement in Miami is corrupt. Five police officers in three different departments were involved in drug dealing in 2017" (right answer: Miami has  4,780 police employees, i.e., 5 corrupt officers are 0.16% of the force).  
 
"Men are toxic! It's crystal clear:  They perpetrate over 76% of the violent crime in the US." (right answer: violent men committing violent crimes constitute 6% of the population of males in the US).

Appeal to Authority: A claim is accepted because not because of its merit, but because of the authority (power, fame, etc) of the person saying it.  

"Pacifism is a good idea because the brilliant scientist Einstein advocated it."

"If the Pope says it, it must be true."  

 "Nobody is a better judge than public opinion."

Red Herring: This fallacy consists in diverting attention from the real issue by focusing instead on an issue having only a surface relevance to the first. 

Daughter: "I'm so hurt that Todd broke up with me, Mom." 
Mother: "Just think of all the starving children in Africa, honey. Your problems will seem pretty insignificant then."

Appeal to Fear: To use threat or harm to advance an argument. Ex: "If we don’t stop petroleum consumption, global warming will increase. Therefore, we need to stop petroleum consumption immediately." 

False Dilemma: It presumes that there are only two alternatives to a given problem, when in fact there are more than two.  

"Either science can explain how she was cured or else, it's a miracle."

"Since there is nothing good on TV tonight, I will just have to get drunk."

"If you are don't accept our climate catastrophe, then you're a denier!"

False Cause: Supposing that two events are connected when in fact they are not. 

"They had a very successful business. Then they decided to adopt a child, and the business went immediately into the red."

Inconsistency: A person commits the fallacy of inconsistency when he or she makes contradictory claims. 

"I'm a strong believer in freedom of speech. However, when a person like John Dean can influence our youth , you have to draw a line and say no more."

"This is the truth: truth is subjective."

Etimological fallacy: Believing that the present day meaning of a word of concept should necessarily be similar to its historical meaning. 

"So-and-so" (a phrase used in the 19th Century) should not be used anymore. It's very offensive! 

Logical and causal possibility (think of mind experiments)

Logical Possiblity:

Something is logically impossible if and only if it violates a law of logic. 

Here is one logical possibility: "President J. F. Kennedy was not killed by Larry Oswald in Texas on November 22, 1963." 

He was indeed killed that day. So, why is it still logically possible? There's no contradiction in assuming Larry Oswald missed his shot or that Kennedy was hurt but survived. 

Causal Possibility:

Something is causally possible if it does not violate law of nature.

Law of non-contradiction: 

Nothing can have and lack property at the same time. 

Examples: "A triangle of four sides," "2 + 2 = 5", "A married bachelor," etc.

Conceivability: 

1. If p is conceivable, it is imaginable (imagination is a mental faculty linked to rationality). An example of that is mind experiments in physics and math. 

Is Superman logically possible? The first step in the evidence that p is possible is to be able to conceive it. Just that. 

We say p is conceivable if its implication can be drawn without it being contradictory, i.e., 

Can Superman be conceived? 

Yes, that's why we talk about him and can even watch him in a movie. 

Now, Clearly, not everything that is conceivable is possible. For example, Superman, dragons, gremlins, and succubi are all conceivable but not possible. 

Why not?  They violate laws of nature.

Remember: If p is conceivable, then from 2. It's logically possible. 

finally,

3. p is causally possible if it doesn't violate a law of nature.  

Now, let's talk a little bit about LAWS OF NATURE: 

Laws differ from scientific theories in that they do not posit a mechanism or explanation of phenomena; they are merely distillations of the results of repeated observation. 

A law's applicability is limited to circumstances resembling those already observed, and the law may be found to be false when extrapolated. 

How do logical possibility (LP) and causal possibility (CP) relate?

If something is logically impossible, it is causally impossible.

If something is causally possible, it is logically possible. 

LI → CI
CP → LP

Clearly, LI is sufficient for CI. Is it necessary? It would be if CI cannot exist without LI. Let's pursue this point further.

Something cannot be and not be at the same time. 

But time is a causal variable, not a logical one. If time is outside us, then "same time" is sort of cheating for a logical category. 

Logic is aprioristic. And yet, Kant has argued that time is not outside. Of course, being a physicist, you will swear that time is outside since you can work with it mathematically. But that doesn't contradict Kant's point (though we don't have time to pursue that here).

¿Qué es la verdad? Grados y tipos de verdad.

En clase les he dicho que la verdad es complicada. Y lo es, pero eso no significa que la filosofía no haya definido el concepto de verdad.

En general tenemos tres definiciones: 

1. Correspondence Theory of Truth (la verdad como correspondencia), 

A proposition is true by its correspondence with reality.  

Ejemplo: Un vertebrado es un animal que tiene un esqueleto con columna vertebral y cráneo, y cuyo sistema nervioso central está formado por la médula espinal y el encéfalo.

2. The Coherence Theory of Truth (la verdad como coherencia con lo que ya se cree).

Truth is what best coheres with our existing knowledge. 

Ejemplo: En cosmología, se entiende por Big Bang,​ o Gran Explosión,​ al comienzo del universo, es decir, el punto inicial en el que se formó la materia, el espacio y el tiempo. 

3. The Pragmatic Theory of Truth (la verdad pragmática).

Truth is, whatever best does the job at hand.  

Ejemplo: El cuadro Guernica de Picasso es una obra maestra de la pintura del siglo XX. 

LA PARADOJA DEL ARGUMENTO AI DE ANTHROPIC

Qué tal si discutimos (después del examen, claro) algo que he descubierto, muy metido en los razonamientos de expertos en IA?  

El argumento de los empleados de Anthropic se basa en dos premisas. La primera:

«La IA será muchísimo más inteligente que nosotros. Por consiguiente, podrá desarrollar estrategias que no podemos comprender.»

La segunda:

«Podemos anticipar que la IA desarrollará estrategias de engaño, supervivencia, adquisición de poder y, eventualmente, destrucción humana.»

OBSERVEN lo que ha ocurrido:

En la primera premisa se nos dice que las estrategias de una inteligencia superior escaparán a nuestra comprensión.

Pero en la segunda comenzamos a describir con precisión cuáles serán esas estrategias.

¿Ven la tensión?

Se las escribo:

«La IA es incognoscible cuando necesitamos justificar el peligro, pero cognoscible cuando necesitamos describirlo»

¿O una cosa o la otra?

¿O ambas a la vez?

Si son ambas, entonces tenemos que explicar qué podemos saber sobre una inteligencia que, por definición, hemos declarado incapaz de ser comprendida. 😁

EJERCICIOS DE LOGICAL & CAUSAL POSSIBILITY & CONCEIVABILITY

Logical Possibility 

Instrucción: Determine whether each statement describes something logically possible or logically impossible. Explain briefly. 

1. A person is 500 years old. ¿Lógicamente posible o imposible? ¿Por qué? 

 2. A square has four sides and three sides at the same time. ¿Lógicamente posible o imposible? ¿Qué principio está involucrado? 

 3. George Washington was never president of the United States. ¿Lógicamente posible o imposible? Clave para el estudiante: Aquí hay una distinción importante: algo puede ser falso sin ser lógicamente imposible. 

Causal Possibility

Instrucción: Determine whether each situation is causally possible or causally impossible, assuming the currently accepted laws of nature. 

1. A person jumps from a building and falls upward into the sky without any external force acting on them. ¿Causalmente posible o imposible? ¿Por qué? 

2. A person travels from New York to London in one second using a machine that moves faster than light. ¿Causalmente posible o imposible? 

3. A person survives for several minutes without breathing. ¿Causalmente posible o imposible? 

Conceivability 

Instrucción: Determine whether the situation is conceivable or inconceivable. Give a reason. 

 1. Imagine a world in which humans have wings and can fly. ¿Concebible o inconcebible? 

 2. Imagine a triangle with four sides. ¿Concebible o inconcebible? 

 3. Imagine that tomorrow the Sun rises in the west. ¿Concebible o inconcebible? 

Law of Non-Contradiction 

Instrucción: Determine whether each statement violates the law of non-contradiction. 

 1. “This object is completely red and completely not red at the same time and in the same respect.” ¿Viola el principio? ¿Por qué? 

 2. “John is married and John is unmarried.” ¿Es necesariamente una contradicción? Explica qué información adicional necesitaríamos. 

 3. “This number is both even and odd.” ¿Viola el principio de no contradicción? 

Put Them Together 

Para cada caso, indique si es: 

A. Lógicamente posible


B. Lógicamente imposible


C. Causalmente posible


D. Causalmente imposible


E. Concebible


F. Inconcebible Puede haber más de una respuesta correcta. 

1. Dragons exist on another planet. 

2. A married bachelor exists. 

3. A human being lives to be 200 years old. 

4. 2 + 2 = 5. 

 5. A person travels back in time.

¿Qué es un experimento mental? (mind experiment)

DEF: The description of a possible situation in which a concept should apply or a condition should be met if the theory in question is true.

Es decir, un experimento mental es un recurso de la imaginación empleado para investigar la naturaleza de las cosas. La mente es el laboratorio del filósofo. Mind experiments nos ayudan a ver y concebir las condiciones de posibilidad de las cosas.

Varias teorías o posturas filosóficas se fundan en los resultados de experimentos mentales: 

el dilema del tranvía,  en ética,

la tabla de Carneades, en ética,

la habitación china,  en filosofía de la mente,

la tierra gemela, en filosofía del lenguaje, 

el cerebro en una cubeta y...

el cuarto de Mary en filosofía de la mente.

Here is an example of how to build a mind experiment.

CONTRA EL PRESENTISMO

El presente no es más verdadero por ser presente. 

Un acontecimiento no adquiere más realidad por encontrarse más cerca de nosotros en el tiempo, del mismo modo que tampoco "pierde realidad" por haber ocurrido hace siglos.

Ser ahora no le confiere privilegio alguno de verdad.

El presentismo introduce una confusión entre actualidad y verdad. 

Lo actual es aquello que comparece ahora, pero esa comparecencia nunca agota lo real. Lo real no se esfuma con el paso del tiempo.

El pasado fue real precisamente porque aconteció, y ese carácter tiene una realidad irrevocable. 

Que ese momento no esté presente ahora significa que ha cambiado su norma de comparecencia, no que haya disminuido en su escala de realidad.

El pasado no puede ser arcaico en el sentido de «inferior», «carente» o «incompleto». 

«Antiguo» y «carente» no son sinónimos. 

El orden temporal no tiene una valoración denominada «carente». Una sociedad posterior a la nuestra, del siglo XXI, puede disponer de mayores conocimientos técnicos y, sin embargo, no ser por ello "superior" en todos los aspectos de su existencia. 

El presente puede saber más sobre algunas cosas y comprender menos sobre otras. 

La historia no es una marcha en la que cada presente corrige y supera al anterior. 

De ser así, lo «posterior» aparecería como más verdadero por el solo hecho de serlo. 

La posterioridad es una relación temporal, no un criterio de verdad.

Si el presente tiene actualidad; el pasado tiene irrevocabilidad. 

Ninguno de los dos posee más verdad que el otro.

HOMEWORK # 2.5

I. PREGUNTAS SOBRE EL CONSENSO

Basado en este post. 

a) Contrast Galen and Vesalius' theories. Was Galen's anatomical view archaic in 1343? In 1443? If not, explain why not.  

b) Why do you think people in the early Middle Ages would accept Galen's view? 

c) What sort of mind experiment would you put forward to make someone understand why something can be valid in 1343 and not in 1543? (Explain answers; take no less than 35 words).

II. PREGUNTAS SOBRE CAUSACIÓN

1. A student studied for the examination and subsequently received a high grade. The student concludes that studying caused the high grade.

2. A person takes a sleeping pill and falls asleep twenty minutes later. They conclude that the pill caused their sleep.

3. A city installs speed cameras, and the number of speeding violations subsequently falls. Officials conclude that the cameras caused the decline.

4. Every time Maria drinks coffee in the afternoon, she has difficulty falling asleep that night. She concludes that the coffee causes her insomnia.

5. A person develops a headache shortly after spending several hours in front of a computer. They conclude that the computer screen caused the headache.

6. A town experiences an unusually hot summer. During the same period, both electricity consumption and ice cream sales increase. Someone concludes that increased ice-cream consumption caused increased electricity consumption.

7. Read the following paragraph and answer the questions below:

A powerful tsunami destroyed the Fukushima Daiichi Nuclear Plant’s power supply and cooling systems, causing three reactors to melt and spew large amounts of radiation. Highly contaminated cooling water applied to the damaged reactors has leaked continuously into building basements and mixed with groundwater. Initial reports of casualties following the tsunami at Fukushima’s power plant put the death toll in the hundreds, with hundreds more missing. 

Was the tsunami the cause of the Daiichi Nuclear Plant’s accident? Yes, No? Explain your answer one way or the other. 

III. Read this short NPR article. 

We find this declaration: 

“We have no evidence that the crew did anything wrong,” Homendy said.

(a) Does that mean there’s no human cause linked to the accident? Explain. 

(b) Are safety regulations, in this case, solely dependent upon human error? Explain. 

Read this paragraph: 

The overheating triggered an alarm, which caused the train’s engineer to immediately apply the brakes to bring the train to the stop. An automatic emergency braking system also came into effect. 

Which of these two caused the train to stop, the overheating or/and the automatic emergency breaking?  

(a) The overheating caused the train’s engineer to immediately apply the brakes to bring the train to a stop, or (b) simultaneously, an automatic emergency braking system also came into effect? 

Read this sentence: 

“There were no reported fatalities or injuries caused directly by the derailment, and responders were able to mitigate the fire within two days.” 

What do you think “caused directly by the derailment” means? 

Read this paragraph: 

“The evacuation order was lifted on Feb. 8, five days after the derailment. Since then, residents have reported widespread concern about the safety of East Palestine’s air and water. Some say they have experienced headaches or rashes. The Ohio Department of Natural Resources reported that some 3,500 fish had died following the derailment in nearby waterways.” 

Do you think the headaches and rashes are the effects of the accident? If so, what is the cause (as given in the reading? 

Read this paragraph: 

“The operators of a Norfolk Southern train carrying hazardous chemicals near East Palestine, Ohio, earlier this month tried to stop the train after a wheel bearing overheated to a dangerous degree, the National Transportation Safety Board said.” 

Can one say that “trying to stop the train after a wheel bearing overheated to a dangerous degree” is the cause of the derailment?

CONSENSO Y SUS LÍMITES

El consenso científico es el acuerdo colectivo, la posición y la opinión de la comunidad científica en un campo de estudio particular en un momento dado.

No significa que todos los científicos estén de acuerdo de forma unánime. Significa que la gran mayoría de los expertos ha evaluado las pruebas disponibles y ha llegado a la misma conclusión general mediante el método científico.

El consenso se logra mediante la acumulación TEMPORAL de evidencia.

Evidencia empírica: Experimentos replicables y observaciones rigurosas. 

Debate abierto: Discusión pública de los datos en congresos y revistas científicas.

El debate no puede ni subestimarse, ni suprimirse ni objetarse. 

Por qué el consenso científico CAMBIA?

1. Aparición de nueva evidencia,  

2. La tecnología mejora, 

3. Se inventan nuevos instrumentos de medición más precisos, 

4. Aparecen datos que antes eran imposibles de detectar, 

5. Nuevos marcos teóricos: A veces, los datos antiguos se explican mejor con una idea completamente nueva. 

AHORA BIEN: Que el consenso pueda cambiar no significa que cualquier opinión alternativa sea válida.